二阶非线性椭圆偏微分方程Dirichlet问题的粘性解(英文)

Uniqueness and Existence of Viscosity Solution on the Dirichlet Problem for Nonlinear Elliptic Second Order Equations

研究了一类二阶非线性椭圆偏微分方程Dirichlet问题粘性解的存在性与唯一性 .首先建立粘性解的比较定理 ,确保了解的唯一性 ,然后运用Perron方法构造出解 .从而解决了这类问题的粘性解的存在性与唯一性 .

In this paper, we investigate the uniqueness and existence of the Dirichlet problem for Nonlinear Second Order Equations: functions of the eigenvalues of the Hessian with the theory of viscosity solution. First, we establish the comparison theorem. Then, we construct the solution of this problem with the Perron′s method. From the above results, the uniqueness and existence of solution will be obtained.